SC Colloquium: "Function Registration and its Applications"
In this talk, I will present my research on function registration and its applications over the past few years. Focusing on statistical modeling for functional data, we have recently developed a novel geometric framework to compare, align, average, and model a collection of random functional observations, where the key step is to find an optimal time warping between two functions for a feature-to-feature alignment. This framework is based on extending the nonparametric version of the Fisher-Rao Riemannian metric to general function spaces, and relies on the fact that this metric is invariant to identical warpings of its arguments. The theoretical underpinning of this new method is established by proving the consistency under a semi-parametric model. We demonstrate this new framework using experimental data in various application domains such as ECG bio-signals, proteomics data, 3D protein structures. Finally, I will present the latest research problems we are working on under the new registration framework.